few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Thought: This problem applies trigonometric identities, including the angle addition formula for cosine.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS
options: Measure and estimate lengths in standard units.

Tell and write time.

Relate addition and subtraction to length.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Classify objects and count the number of objects in each category.

Describe and compare measurable attributes.

Represent and interpret data.

Measure lengths indirectly and by iterating length units.

Geometric measurement: understand concepts of angle and measure angles.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Work with time and money.

Convert like measurement units within a given measurement system.
problem_activity: Narrative
The purpose of this activity is for students to measure lengths using a ruler that is marked with half inches and quarter inches. Building on their understanding of equivalent fractions, students recognize that lengths that line up with a half-inch mark can be read as one-half of an inch or two-fourths of an inch. They also recognize that lengths that are whole numbers of inches can be expressed as fractions.
MLR8 Discussion Supports.
Synthesis: Provide students with the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking
Required Materials
Materials to Gather
Materials from a previous activity
Rulers (inches)
Required Preparation
Each student needs a ruler marked with half inches and quarter inches from the warm-up.
Launch
Groups of 2
Display the problem.
“Think about how Kiran and Jada record the length of the worm. Use the ruler to explain how both of their measurements make sense.”
1 minute: quiet think time
2–3 minutes: partner discussion
Monitor for students that say they both make sense because
\(4\frac{1}{2}\)
is equivalent to
\(4\frac{2}{4}\)
and select them to share their responses.
Make sure each student has a ruler marked with half inches and quarter inches from the previous activity.
Activity
“Now, work with your partner to measure the length of some worms. Some lengths can be recorded in more than one way. Be ready to explain how you recorded each length.”
3–5 minutes: partner work time
Student Facing
Kiran and Jada are discussing the length of a worm.
[IMG]
[IMG]
Kiran says that the worm is
\(4\frac{2}{4}\)
inches long.
Jada says that the worm is
\(4\frac{1}{2}\)
inches long.
Use the ruler to explain how both of their measurements are correct.
Measure the length of the following worms.
A
[IMG]
B
[IMG]
C
[IMG]
D
[IMG]
Student Response
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Advancing Student Thinking
If students start measuring from the edge of their ruler instead of from 0, consider asking:
“In the image for the first problem, how is the ruler lined up to the worm?”
“Why does it make sense to not line up the left end of the ruler with the left end of the worm?”
Activity Synthesis
Invite students to share how they recorded their measurements and why they chose to record them in the way they did.
“Let’s think more about the first worm you measured. What are all the ways that we could record its length?” (4 inches.
\(\frac{8}{2}\)
inches.
\(\frac{16}{4}\)
inches.)
“What are all the ways that we could record the length of the last worm?” (
\(3\frac{1}{2}\)
inches.
\(3\frac{2}{4}\)
inches.
\(\frac{7}{2}\)
inches.
\(\frac{14}{4}\)
inches.)
“We can use different numbers to describe the same length because the numbers are equivalent.”


correct_option_index: 9